G. Van Hoven

Creation of current filaments in the solar corona

It has been suggested that the solar corona is heated by the dissipation of electric currents. The low value of the resistivity requires the magnetic field to have structure at very small length scales if this mechanism is to work. In this paper it is demonstrated that the coronal magnetic field acquires small-scale structure through the braiding produced by smooth, randomly phased, photospheric flows. The current density develops a filamentary structure and grows exponentially in time. Nonlinear processes in the ideal magnetohydrodynamic equations produce a cascade effect, in which the structure introduced by the flow at large length scales is transferred to smaller scales. If this process continues down to the resistive dissipation length scale, it would provide an effective mechanism for coronal heating.

The stability of coronal loops - Finite-length and pressure-profile limits

Results are described from a quickly converging, necessary-and-sufficient, MHD-stability test for coronal-loop models. The primary stabilizing influence arises from magnetic line tying at the photosphere, and this end conditions requires a series expansion of possible loop excitations. The stability boundary is shown to quickly approach a limit as the number of terms increases, providing a critical length for the loop in proportion to its transverse magnetic scale. Several models of force-free-field profiles are tested and the stability behavior of a localized current channel, embedded in an external current-free region, is shown to be superior to that of other, broader, current profiles. Pressure-gradient effects, leading to increased or decreased stability, are shown to be amplified by line tying. Long loops must either conduct low net current, or exhibit an axial-field reversal coexisting with a low-pressure core. The limits on stability depend on the magnetic aspect ratio, the plasma-to-magnetic pressure ratio, and the field orientation at the loop edge. Applications of these results to the structure of coronal loops are described.

The growth of the tearing mode: Boundary and scaling effects

The linear development of the resistive tearing instability in a sheet pinch is investigated numerically. Particular emphasis is placed on effects which differentiate magnetic tearing in astrophysical situations from that in laboratory devices. These include extreme values of the parameters determining the mode growth and a variety of boundary conditions. Eigenfunction profiles for long and short wavelengths are computed and the applicability of the ‘‘constant Ψ’’ approximation is investigated. Nearby conducting walls tend to validate this condition and reduce the growth rate, especially for the long wavelength modes which, otherwise, disturb a larger region of the plasma than do short wavelength modes. Finally, the growth rate p is computed for values of the magnetic Reynolds number S up to 1012 and of the dimensionless wavelength parameter α down to 10−3. The results demonstrate, without approximation, the S2/5 scaling of p at large α (constant Ψ) and the S2/3 scaling at small α (nonconstant‐Ψ). The α a...

Prominence formation in a coronal loop

A model is presented which depends on the preferential deposition of heating in the legs of a coronal loop and which produces a stable prominence-scale condensation at the loop top. Dynamic stability is attained by the subsequent adjustment of local parallel gravity by a magnetic inversion at the loop (or arcade) apex. A nonlinear numerical simulation of this process, which includes a deep chromosphere, a heating rate with a fixed dissipation length, and full solar gravity is described. 12 refs.

Radiative instabilities in a sheared magnetic field

The structure and growth rate of the radiative instability in a sheared magnetic field B have been calculated analytically using the Braginskii fluid equations. In a shear layer, temperature and density perturbations are linked by the propagation of sound waves parallel to the local magnetic field. As a consequence, density clumping or condensation plays an important role in driving the instability. Parallel thermal conduction localizes the mode to a narrow layer where k∥ =k⋅B/‖B‖ is small and stabilizes short wavelengths k>kc, where kc depends on the local radiation and conduction rates. Thermal coupling to ions also limits the width of the unstable spectrum. It is shown that a broad spectrum of modes is typically unstable in tokamak edge plasmas and it is argued that this instability is sufficiently robust to drive the large‐amplitude density fluctuations often measured there.

Radiative tearing - Magnetic reconnection on a fast thermal-instability time scale

Two energy modification mechanisms which are known to occur in sheared magnetic fields are the tearing and thermal instabilities. These processes can be studied separately with formalisms incorporating just the effective driving mechanism of interest (finite resistivity for the tearing mode and unstable radiation for the thermal mode). A model which includes both effects, and a temperature-dependent resistivity, indicates that modified forms of these two instabilities may coexist for identical physical conditions. When they are isolated computationally, one can show that their limiting growth rates are approximately those of the uncoupled instabilities. The spatial structure and energy content of these two new hybrid processes are then individually examined and are found to differ considerably from those obtained from separate treatments of the driving mechanisms. The faster radiative instability, which has a hydromagnetically scaled growth rate like the condensation mode of the thermal instability, is shown to involve a substantial amount of magnetic field reconnection. This can be partially explained by a large temperature drop (or resistivity rise) at the X-point. The island width of the Coulomb-coupled radiative mode is 30 percent of that produced by a comparable level of the slower tearing instability. In addition, the perturbed magnetic energy in the radiative instability is 5 times that of the perturbed thermal energy, indicating an appreciable modification of the initial magnetic structure.

The thermal instability in a sheared magnetic field - Filament condensation with anisotropic heat conduction

The condensation-mode growth rate of the thermal instability in an empirically motivated sheared field is shown to depend upon the existence of perpendicular thermal conduction. This typically very small effect (perpendicular conductivity/parallel conductivity less than about 10 to the -10th for the solar corona) increases the spatial-derivative order of the compressible temperature-perturbation equation, and thereby eliminates the singularities which appear when perpendicular conductivity = 0. The resulting growth rate is less than 1.5 times the controlling constant-density radiation rate, and has a clear maximum at a cross-field length of order 100 times and a width of about 0.1 the magnetic shear scale for solar conditions. The profiles of the observable temperature and density perturbations are independent of the thermal conductivity, and thus agree with those found previously. An analytic solution to the short-wavelength incompressible case is also given.

Coronal loop formation resulting from photospheric convection

We have demonstrated the dynamic formation of coronal magnetic loops in three dimensions as a result of horizontal vortex-like convection on the photosphere. Localized plasma motions twist bipolar magnetic field lines which are tied to the dense photosphere by high electrical conductivity. The twists propagate into the corona along the field and create a narrow quasi-toroidal region where the field lines interwind. At the same time, this tubeline region rises in altitude, expands in cross section, and distorts into a slight S shape before settling into an equilibrium state. The MHD stability of such line-tied magnetic loop structures is directly exhibited by this dynamic simulation.

Nonlinear radiative condensation in a sheared magnetic field

A well-resolved two-dimensional nonlinear numerical simulation of the radiative/thermal instability in a sheared magnetic field is described which leads to filament formation. The condensation is initiated by a linearly unstable mode and widens until it is slowed by thermal conduction parallel to B. During the nonlinear evolution, the minimum temperature falls from 10 to the 6th K to 10 to the 4th K and eventually reaches a state of local thermal equilibrium in about five e-folding times. 13 references.

Ideal condensations due to perpendicular thermal conduction in a sheared magnetic field

Cool condensations generated by a radiative thermal instability in a sheared magnetic field have previously been the bases of solar filament formation models. Through the assumption of fully anisotropic heat flow, a new set of condensation modes are here obtained which become singular in the limit of vanishing perpendicular thermal conductivity. The growth rates are noted to typically be greater than those reported previously for sheared field condensations. The fastest growth is exhibited by modes possessing the fewest oscillations.